Abstract
Let K be the function field of a smooth projective surface S over a finite field \( \mathbb{F}\). In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in \( {H}^{3}(K, \mathbb{Z}/\ell)\) by elements in \( {H}^{2}(K, \mathbb{Z}/\ell), {l} \neq car.K \).
Mathematics Subject Classiffication (2010). 12G05, 11G25, 14J20.
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Pirutka, A. (2017). On a Local-Global Principle for H 3 of Function Fields of Surfaces over a Finite Field. In: Auel, A., Hassett, B., Várilly-Alvarado, A., Viray, B. (eds) Brauer Groups and Obstruction Problems . Progress in Mathematics, vol 320. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-46852-5_10
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DOI: https://doi.org/10.1007/978-3-319-46852-5_10
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